Analysis of an k-out-of-n:G system with redundant dependency and repair equipment procurement

ABSTRACT

This paper studies an k-out-of-n:G system with redundant dependency and repair equipment procurement lead time where the operating times and repair times of components follow exponential distributions and phase-type distributions, respectively. When one component breaks down, it is repaired by a repair equipment. The repair equipment may fail during the repair period and the following repair is not ‘as good as new’. After a number of repairs, it is replaced by a new one. The new spare repair equipment for replacement is only available by an order, and the procurement lead time for delivering follows a phase-type distribution. Moreover, in the multi-component system, the redundant dependency is taken into account. Applying the matrix-analytical method, the system availability, the rate of occurrence of failures of the system, the expected number of broken components, the availability and the rate of occurrence of failures of the repair equipment are derived. Finally, numerical examples are given to show these theoretical results.

Keywords:

• k-out-of-n:G system
• redundant dependency
• procurement lead time
• matrix-analytical method
• reliability measures

Acknowledgements

The authors acknowledge anonymous reviewers for their constructive comments which are very helpful in improving the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [grantnumber 72001181], [grant number 71571127] and the funding of V.C. & V.R. Key Lab of Sichuan Province (SCVCVR2019.05VS).

Notes on contributors

Wenqing Wu

Wenqing Wu was born in 1986. He obtained both M.S. and D.Sc degree in Applied Mathematics from Sichuan Normal University, Chengdu, China, in 2012 and 2015, respectively. His current research interests include reliability analysis, queueing theory and grey forecasting models. E-mail: [email protected].

Kai Zuo

Kai Zuo received both M.S. and D.Sc degree in Applied Mathematics from Sichuan Normal University, Chengdu, China, in 2012 and 2017, respectively. His current research interests include fuzzy theory, forecasting and reliability. E-mail: [email protected].

Yinghui Tang

Yinghui Tang is a professor in the School of Mathematical Sciences, Sichuan Normal University, Chengdu, China. He received his PhD degree in Operational Research from Sichuan University. He has published more than 200 articles in national and international journals of repute. His research interests include stochastic models, reliability analysis and insurance risk theory. E-mail: [email protected].

Yuanyuan Zhang

Yuanyuan Zhang was graduated in Applied Mathematics from Sichuan Normal University. She is working in the school of science of Southwest University of Science and Technology. Her research interests are focused on Reliability and stochastic differential equation. E-mail: [email protected].